erweitern (1+2x+x^2)^6

Lösung

erweitern

(1 + 2 x + x^{2})^{6}

x^{12} + 12 x^{11} + 66 x^{10} + 220 x^{9} + 495 x^{8} + 792 x^{7} + 924 x^{6} + 792 x^{5} + 495 x^{4} + 220 x^{3} + 66 x^{2} + 12 x + 1

Schritte zur Lösung

(1 + 2 x + x^{2})^{6}

(1 + 2 x + x^{2})^{6} = (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2})

= (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1)

Multipliziere aus

(1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) : x^{12} + 12 x^{11} + 66 x^{10} + 220 x^{9} + 495 x^{8} + 792 x^{7} + 924 x^{6} + 792 x^{5} + 495 x^{4} + 220 x^{3} + 66 x^{2} + 12 x + 1

= x^{12} + 12 x^{11} + 66 x^{10} + 220 x^{9} + 495 x^{8} + 792 x^{7} + 924 x^{6} + 792 x^{5} + 495 x^{4} + 220 x^{3} + 66 x^{2} + 12 x + 1

e x p an d (x - 2) 35 6^{^{'}}

e x p an d ln (a x + b) \cdot 2 x \cdot (a x + b)

e x p an d (4 x + 7 y = 3, 7) (3 x - y = 16)

e x p an d [x (x + 1)]^{2}

e x p an d 3 x (3 x + 2 x ln (x))